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Embedding (Commons Math 3.2 API)
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org.apache.commons.math3.geometry.partitioning</FONT>
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Interface Embedding&lt;S extends <A HREF="../../../../../../org/apache/commons/math3/geometry/Space.html" title="interface in org.apache.commons.math3.geometry">Space</A>,T extends <A HREF="../../../../../../org/apache/commons/math3/geometry/Space.html" title="interface in org.apache.commons.math3.geometry">Space</A>&gt;</H2>
<DL>
<DT><DT><B>Type Parameters:</B><DD><CODE>S</CODE> - Type of the embedding space.<DD><CODE>T</CODE> - Type of the embedded sub-space.</DL>
<DL>
<DT><B>All Known Implementing Classes:</B> <DD><A HREF="../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Line.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Line</A>, <A HREF="../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Line.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Line</A>, <A HREF="../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Plane.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Plane</A></DD>
</DL>
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<DL>
<DT><PRE>public interface <B>Embedding&lt;S extends <A HREF="../../../../../../org/apache/commons/math3/geometry/Space.html" title="interface in org.apache.commons.math3.geometry">Space</A>,T extends <A HREF="../../../../../../org/apache/commons/math3/geometry/Space.html" title="interface in org.apache.commons.math3.geometry">Space</A>&gt;</B></DL>
</PRE>

<P>
This interface defines mappers between a space and one of its sub-spaces.

 <p>Sub-spaces are the lower dimensions subsets of a n-dimensions
 space. The (n-1)-dimension sub-spaces are specific sub-spaces known
 as <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Hyperplane.html" title="interface in org.apache.commons.math3.geometry.partitioning"><CODE>hyperplanes</CODE></A>. This interface can be used regardless
 of the dimensions differences. As an example, <A HREF="../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Line.html" title="class in org.apache.commons.math3.geometry.euclidean.threed"><CODE>Line</CODE></A> in 3D
 implements Embedding<<A HREF="../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed"><CODE>Vector3D</CODE></A>, {link
 org.apache.commons.math3.geometry.euclidean.oned.Vector1D Vector1D>, i.e. it
 maps directly dimensions 3 and 1.</p>

 <p>In the 3D euclidean space, hyperplanes are 2D planes, and the 1D
 sub-spaces are lines.</p>
<P>

<P>
<DL>
<DT><B>Since:</B></DT>
  <DD>3.0</DD>
<DT><B>Version:</B></DT>
  <DD>$Id: Embedding.java 1416643 2012-12-03 19:37:14Z tn $</DD>
<DT><B>See Also:</B><DD><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Hyperplane.html" title="interface in org.apache.commons.math3.geometry.partitioning"><CODE>Hyperplane</CODE></A></DL>
<HR>

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<CODE>&nbsp;<A HREF="../../../../../../org/apache/commons/math3/geometry/Vector.html" title="interface in org.apache.commons.math3.geometry">Vector</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Embedding.html" title="type parameter in Embedding">S</A>&gt;</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Embedding.html#toSpace(org.apache.commons.math3.geometry.Vector)">toSpace</A></B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/Vector.html" title="interface in org.apache.commons.math3.geometry">Vector</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Embedding.html" title="type parameter in Embedding">T</A>&gt;&nbsp;point)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Transform a sub-space point into a space point.</TD>
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<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../../org/apache/commons/math3/geometry/Vector.html" title="interface in org.apache.commons.math3.geometry">Vector</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Embedding.html" title="type parameter in Embedding">T</A>&gt;</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Embedding.html#toSubSpace(org.apache.commons.math3.geometry.Vector)">toSubSpace</A></B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/Vector.html" title="interface in org.apache.commons.math3.geometry">Vector</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Embedding.html" title="type parameter in Embedding">S</A>&gt;&nbsp;point)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Transform a space point into a sub-space point.</TD>
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<A NAME="toSubSpace(org.apache.commons.math3.geometry.Vector)"><!-- --></A><H3>
toSubSpace</H3>
<PRE>
<A HREF="../../../../../../org/apache/commons/math3/geometry/Vector.html" title="interface in org.apache.commons.math3.geometry">Vector</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Embedding.html" title="type parameter in Embedding">T</A>&gt; <B>toSubSpace</B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/Vector.html" title="interface in org.apache.commons.math3.geometry">Vector</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Embedding.html" title="type parameter in Embedding">S</A>&gt;&nbsp;point)</PRE>
<DL>
<DD>Transform a space point into a sub-space point.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>point</CODE> - n-dimension point of the space
<DT><B>Returns:</B><DD>(n-1)-dimension point of the sub-space corresponding to
 the specified space point<DT><B>See Also:</B><DD><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Embedding.html#toSpace(org.apache.commons.math3.geometry.Vector)"><CODE>toSpace(org.apache.commons.math3.geometry.Vector<T>)</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="toSpace(org.apache.commons.math3.geometry.Vector)"><!-- --></A><H3>
toSpace</H3>
<PRE>
<A HREF="../../../../../../org/apache/commons/math3/geometry/Vector.html" title="interface in org.apache.commons.math3.geometry">Vector</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Embedding.html" title="type parameter in Embedding">S</A>&gt; <B>toSpace</B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/Vector.html" title="interface in org.apache.commons.math3.geometry">Vector</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Embedding.html" title="type parameter in Embedding">T</A>&gt;&nbsp;point)</PRE>
<DL>
<DD>Transform a sub-space point into a space point.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>point</CODE> - (n-1)-dimension point of the sub-space
<DT><B>Returns:</B><DD>n-dimension point of the space corresponding to the
 specified sub-space point<DT><B>See Also:</B><DD><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Embedding.html#toSubSpace(org.apache.commons.math3.geometry.Vector)"><CODE>toSubSpace(org.apache.commons.math3.geometry.Vector<S>)</CODE></A></DL>
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